$$35x^5y^4-25x^4 \cdot \dfrac{y^3}{5}x^2y^2=\dfrac{-25x^6y^5+175x^5y^4}{5}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}35x^5y^4-25x^4\frac{y^3}{5}x^2y^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}35x^5y^4-\frac{25x^4y^3}{5}x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}35x^5y^4-\frac{25x^6y^3}{5}y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}35x^5y^4-\frac{25x^6y^5}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-25x^6y^5+175x^5y^4}{5}\end{aligned} $$ | |
| ① | Multiply $25x^4$ by $ \dfrac{y^3}{5} $ to get $ \dfrac{ 25x^4y^3 }{ 5 } $. Step 1: Write $ 25x^4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 25x^4 \cdot \frac{y^3}{5} & \xlongequal{\text{Step 1}} \frac{25x^4}{\color{red}{1}} \cdot \frac{y^3}{5} \xlongequal{\text{Step 2}} \frac{ 25x^4 \cdot y^3 }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^4y^3 }{ 5 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{25x^4y^3}{5} $ by $ x^2 $ to get $ \dfrac{ 25x^6y^3 }{ 5 } $. Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{25x^4y^3}{5} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{25x^4y^3}{5} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25x^4y^3 \cdot x^2 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^6y^3 }{ 5 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{25x^6y^3}{5} $ by $ y^2 $ to get $ \dfrac{ 25x^6y^5 }{ 5 } $. Step 1: Write $ y^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{25x^6y^3}{5} \cdot y^2 & \xlongequal{\text{Step 1}} \frac{25x^6y^3}{5} \cdot \frac{y^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25x^6y^3 \cdot y^2 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^6y^5 }{ 5 } \end{aligned} $$ |
| ④ | Subtract $ \dfrac{25x^6y^5}{5} $ from $ 35x^5y^4 $ to get $ \dfrac{ \color{purple}{ -25x^6y^5+175x^5y^4 } }{ 5 }$. Step 1: Write $ 35x^5y^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |